Question

adding and subtracting rational expressions quiz
algebra 2 a ae teacher (acc ed) / module 6; rational functions and r

1. what is the difference of \\(\frac{5x}{x^2 + 6x + 8} - \frac{3}{x^2 + 7x + 10}\\)?

\\(\frac{5x^2 - 22x - 12}{(x + 2)(x + 4)(x + 5)}, x \
eq -2, x \
eq -4, x \
eq -5\\)
\\(\frac{5x - 3}{(x + 2)(x + 4)(x + 5)}, x \
eq -2, x \
eq -4, x \
eq -5\\)
\\(\frac{5x^2 + 22x + 12}{(x + 2)(x + 4)(x + 5)}, x \
eq -2, x \
eq -4, x \
eq -5\\)
\\(\frac{5x^2 + 22x - 12}{(x + 2)(x + 4)(x + 5)}, x \
eq -2, x \
eq -4, x \
eq -5\\)

Explanation:

Step1: Factor denominators

$x^2+6x+8=(x+2)(x+4)$; $x^2+7x+10=(x+2)(x+5)$

Step2: Find common denominator

Common denominator: $(x+2)(x+4)(x+5)$

Step3: Rewrite fractions

$\frac{5x(x+5)}{(x+2)(x+4)(x+5)} - \frac{3(x+4)}{(x+2)(x+4)(x+5)}$

Step4: Expand numerators

$5x(x+5)=5x^2+25x$; $3(x+4)=3x+12$

Step5: Subtract numerators

$5x^2+25x - 3x -12=5x^2+22x-12$

Step6: Combine into one fraction

$\frac{5x^2+22x-12}{(x+2)(x+4)(x+5)}$ with restrictions $x
eq-2,-4,-5$

Answer:

$\frac{5x^2 + 22x - 12}{(x+2)(x+4)(x+5)}, x
eq -2, x
eq -4, x
eq -5$